Can We Understand Our Own Minds or Brains?
The other metaphorical analogue to Godel's Theorem which I find pro-
vocative suggests that ultimately, we cannot understand our own minds/
brains. This is such a lo:tded, many-leveled idea that one must be extremely
cautious in proposing it. What does "understanding our own mindslbrains"
mean? It could mean having a general sense of how they work, as
mechanics have a sense of how cars work. It could mean having a complete
explanation for why people do any and all things they do. It could mean
having a complete understanding of the physical structure of one's own
brain on all levels. It could mean having a complete wiring diagram of a
brain in a book (or library or computer). It could mean knowing, at every
instant, precisely what is happening in one's own brain on the neural
level--each firing, each synaptic alteration, and so on. It could mean having
written a program which passes the Turing test. It could mean knowing
oneself so perfectly that such notions as the subconscious and the intuition
make no sense, because everything is out in the open. It could mean any
number of other things.
Which of these types of self-mirroring, if any, does the self-mirroring
in GOdel's Theorem most resemble? I would hesitate to say. Some of them
are quite silly. For instance, the idea of being able to monitor your own
brain state in all its detail is a pipe dream, an absurd and uninteresting
proposition to start with; and if Godel's Theorem suggests that it is impos-
sible, that is hardly a revelation. On the other hand, the age-old goal of
knowing yourself in some profound way-let us call it "understanding your
own psychic structure"-has a ring of plausibility to it. But might there not
be some vaguely Godelian loop which limits the depth to which any indi-
vidual can penetrate into his own psyche? Just as we cannot see our faces
with our own eyes, is it not reasonable to expect that we cannot mirror our
complete mental structures in the symbols which carry them out?
All the limitative Theorems of metamathematics and the theory of
computation suggest that once the ability to represent your own structure
has reached a certain critical point, that is the kiss of death: it guarantees
that you can never represent yourself totally. Godel's Incompleteness The-
orem, Church's Undecidability Theorem, Turing's Halting Theorem,
Tarski's Truth Theorem-all have the flavor of some ancient fairy tale
which warns you that "To seek self-knowledge is to embark on a journey
which ... will always be incomplete, cannot be charted on any map, will
never halt, cannot be described."
But do the limitative Theorems have any bearing on people? Here is
one way of arguing the case. Either I am consistent or I am inconsistent.
(The latter is much more likely, but for completeness' sake, I consider both
possibilities.) If I am consistent, then there are two cases. (1) The "low-
fidelity" case: my self-understanding is below a certain critical point. In this
case, I am incomplete by hypothesis. (2) The "high-fidelity" case: My
self-understanding has reached the critical point where a metaphorical
analogue of the limitative Theorems does apply, so my self-understanding
Strange Loops, Or Tangled Hierarchies^697